Details

sample93.0ms

Algorithm

intervals

Results

44.0ms	110×	body	1280	valid
21.0ms	24×	body	2560	valid
13.0ms	56×	body	640	valid
5.0ms	32×	body	320	valid
1.0ms	27×	body	80	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize13.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.9b	(sin (+ x eps))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

24.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.3s

Counts

46 → 46

Iterations

Useful iterations: 3 (441.0ms)

Iter	Nodes	Cost
0	91	662
1	189	539
2	472	452
3	1618	388
done	5000	388

prune109.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`fma-def` `distribute-lft-out`
3×	`expm1-log1p-u` `associate-r` `associate-l` `sum-log` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

15.0ms	(+ (+ x eps) x)
16.0ms	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
21.0ms	(cos (/ (+ (+ x eps) x) 2))

series93.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
48.0ms	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

60 → 60

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	99	768
1	227	695
2	572	615
3	1507	551
done	5001	550

prune180.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
21.0ms	(cos (/ (+ (+ x eps) x) 2))
4.0ms	(cos (/ (fma 2 x eps) 2))
2.0ms	(cos (/ (fma 2 x eps) 2))

series146.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
23.0ms	(cos (/ (fma 2 x eps) 2))
24.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.6s

Counts

52 → 52

Iterations

Useful iterations: 4 (247.0ms)

Iter	Nodes	Cost
0	60	597
1	109	582
2	200	512
3	382	479
4	937	463
5	2230	463
done	5001	463

prune232.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
3.9b	(cos (/ (+ (+ x eps) x) 2))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 52

Calls

4 calls:

3.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
21.0ms	(cos (/ (+ (+ x eps) x) 2))
2.0ms	(cos (/ (fma 2 x eps) 2))
2.0ms	(cos (/ (fma 2 x eps) 2))

series117.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
22.0ms	(cos (/ (+ (+ x eps) x) 2))
24.0ms	(cos (/ (fma 2 x eps) 2))
24.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.5s

Counts

64 → 64

Iterations

Useful iterations: 3 (297.0ms)

Iter	Nodes	Cost
0	73	763
1	160	680
2	417	618
3	1987	604
done	5000	604

prune268.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

regimes125.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.1b

bsearch135.0ms

Steps

Iters	Range		Point
11	2.28145452431431e-18	2231369.5462890854	1.174838876346265e-08
10	-925426.909356872	-1.1036397448000079e-07	-1.1161292204334507e-07

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	53
1	38	38
done	38	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3333×	body	1280	valid
608.0ms	666×	body	2560	valid
451.0ms	1791×	body	640	valid
119.0ms	779×	body	320	valid
59.0ms	1083×	body	80	valid
37.0ms	348×	body	160	valid